SOLUTION: What is the range of y=2x-7x^2?

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Question 1108738: What is the range of y=2x-7x^2?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=2x-7x%5E2 you are given the parabola opens downwards (a is negative number), and it has a maximum at vertex
so, y coordinate of the vertex will be greatest value of the range
now find the coordinates of the vertex:
The x-coordinate of the vertex can be found by the formula -b%2F2a, and to get the y value of the vertex, just substitute -b%2F2a, into the y=2x-7x%5E2
you have a=-7 and b=2
-b%2F2a=-2%2F%282%28-7%29%29=2%2F14=1%2F7
y=2%281%2F7%29-7%281%2F7%29%5E2
y=2%2F7-cross%287%291%281%2Fcross%2849%297%29
y=2%2F7-1%2F7
y=1%2F7
so, the vertex is at (1%2F7,1%2F7)
and the range is:
{ y element R : y%3C=1%2F7 }